How much air pressure is held between an inflated tube and the tire?

Here is the reason why I ask...

I got a flat on Sunday. Super small piece of glass wreaking havoc but leaving a decent size hole in the crown of the tire. I plucked it out, changed the tube with a new one and went on my way. I went out for a ride this morning and got another flat after about 3 miles. Upon examination I realized I failed to get all the glass out.

After getting it clean, changed, and inflated, I noticed a fair amount of air coming out of the small hole in the tire itself (i.e. the spit test). A bit confused I decided not to risk it since I was out of c02 and rubber, so decided to come back. The tire appeared to have held air after the 3 mile trip back.

I'm confused as to why the hole in the tire would be releasing air. Wouldnt a properly inflated tube displace that air? Furthermore if it did have a measurable amount of pressure, wouldnt it escape through more obvious locations such as the hole that houses the valve stem?

Thanks